Theory of variational quantum simulation
The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and simulating real and imaginary time dynamics. In this work, we firs...
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2019-10-01
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Online Access: | https://quantum-journal.org/papers/q-2019-10-07-191/pdf/ |
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doaj-75f7107b3b024ac7bc93222f3390251e2020-11-25T02:28:25ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2019-10-01319110.22331/q-2019-10-07-19110.22331/q-2019-10-07-191Theory of variational quantum simulationXiao YuanSuguru EndoQi ZhaoYing LiSimon C. BenjaminThe variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and simulating real and imaginary time dynamics. In this work, we first review the conventional variational principles, including the Rayleigh-Ritz method for solving static problems, and the Dirac and Frenkel variational principle, the McLachlan's variational principle, and the time-dependent variational principle, for simulating real time dynamics. We focus on the simulation of dynamics and discuss the connections of the three variational principles. Previous works mainly focus on the unitary evolution of pure states. In this work, we introduce variational quantum simulation of mixed states under general stochastic evolution. We show how the results can be reduced to the pure state case with a correction term that takes accounts of global phase alignment. For variational simulation of imaginary time evolution, we also extend it to the mixed state scenario and discuss variational Gibbs state preparation. We further elaborate on the design of ansatz that is compatible with post-selection measurement and the implementation of the generalised variational algorithms with quantum circuits. Our work completes the theory of variational quantum simulation of general real and imaginary time evolution and it is applicable to near-term quantum hardware.https://quantum-journal.org/papers/q-2019-10-07-191/pdf/ |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Xiao Yuan Suguru Endo Qi Zhao Ying Li Simon C. Benjamin |
spellingShingle |
Xiao Yuan Suguru Endo Qi Zhao Ying Li Simon C. Benjamin Theory of variational quantum simulation Quantum |
author_facet |
Xiao Yuan Suguru Endo Qi Zhao Ying Li Simon C. Benjamin |
author_sort |
Xiao Yuan |
title |
Theory of variational quantum simulation |
title_short |
Theory of variational quantum simulation |
title_full |
Theory of variational quantum simulation |
title_fullStr |
Theory of variational quantum simulation |
title_full_unstemmed |
Theory of variational quantum simulation |
title_sort |
theory of variational quantum simulation |
publisher |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
series |
Quantum |
issn |
2521-327X |
publishDate |
2019-10-01 |
description |
The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and simulating real and imaginary time dynamics. In this work, we first review the conventional variational principles, including the Rayleigh-Ritz method for solving static problems, and the Dirac and Frenkel variational principle, the McLachlan's variational principle, and the time-dependent variational principle, for simulating real time dynamics. We focus on the simulation of dynamics and discuss the connections of the three variational principles. Previous works mainly focus on the unitary evolution of pure states. In this work, we introduce variational quantum simulation of mixed states under general stochastic evolution. We show how the results can be reduced to the pure state case with a correction term that takes accounts of global phase alignment. For variational simulation of imaginary time evolution, we also extend it to the mixed state scenario and discuss variational Gibbs state preparation. We further elaborate on the design of ansatz that is compatible with post-selection measurement and the implementation of the generalised variational algorithms with quantum circuits. Our work completes the theory of variational quantum simulation of general real and imaginary time evolution and it is applicable to near-term quantum hardware. |
url |
https://quantum-journal.org/papers/q-2019-10-07-191/pdf/ |
work_keys_str_mv |
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